Seminars and Colloquia by Series

ARC Distinguished Lecture - Algorithmic Pricing

Series
Other Talks
Time
Monday, April 8, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116
Speaker
Avrim Blum – Carnegie Mellon University
Pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare or profit) is a central problem in Algorithmic Mechanism Design. In this talk I will discuss some particularly simple algorithms that are able to achieve surprisingly strong guarantees for a range of problems of this type. As one example, for the problem of pricing resources, modeled as goods having an increasing marginal extraction cost to the seller, a simple approach of pricing the i-th unit of each good at a value equal to the anticipated extraction cost of the 2i-th unit gives a constant-factor approximation to social welfare for a wide range of cost curves and for arbitrary buyer valuation functions. I will also discuss simple algorithms with good approximation guarantees for revenue, as well as settings having an opposite character to resources, namely having economies of scale or decreasing marginal costs to the seller.

Statistical Mechanics of the Two-Dimensional Coulomb Gas

Series
Math Physics Seminar
Time
Friday, April 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pierluigi Falco – California State University, Northridge
The lattice, two dimensional, Coulomb gas is the prototypical model of Statistical Mechanics displaying the 'Kosterlitz-Thouless' phase transition. In this seminar I will discuss conjectures, results and works in progress about this model.

Hypergraph Ramsey Problems

Series
Combinatorics Seminar
Time
Friday, April 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dhruv Mubayi – University of Illinois, Chicago
I will survey the major results in graph and hypergraph Ramsey theory and present some recent results on hypergraph Ramsey numbers. This includes a hypergraph generalization of the graph Ramsey number R(3,t) proved recently with Kostochka and Verstraete. If time permits some proofs will be presented.

Integral homology of hyperbolic three--manifolds

Series
Geometry Topology Seminar
Time
Friday, April 5, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jean Raimbault – Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie
It is a natural question to ask whether one can deduce topological properties of a finite--volume three--manifold from its Riemannian invariants such as volume and systole. In all generality this is impossible, for example a given manifold has sequences of finite covers with either linear or sub-linear growth. However under a geometric assumption, which is satisfied for example by some naturally defined sequences of arithmetic manifolds, one can prove results on the asymptotics of the first integral homology. I will try to explain these results in the compact case (this is part of a joint work with M. Abert, N. Bergeron, I. Biringer, T. Gelander, N. Nikolov and I. Samet) and time permitting I will discuss their extension to manifolds with cusps such as hyperbolic knot complements.

Tutorial: Information-based complexity of convex optimization

Series
ACO Student Seminar
Time
Friday, April 5, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
ISyE Executive classroom
Speaker
Cristobal Guzman – ISyE, Georgia Tech –
Information-based complexity is an alternative to Turing complexity that is well-suited for understanding a broad class of convex optimization algorithms. The groundbreaking work of Nemirovski and Yudin provided the basis of the theory, establishing tight lower bounds on the running time of first-order methods in a number of settings. There has been a recent interest on these classical techniques, because of exciting new applications on Machine Learning, Signal Processing, Stochastic Programming, among others. In this talk, we will introduce the rudiments of the theory, some examples, and open problems. Based on joint work with Gábor Braun and Sebastian Pokutta.

Conormals and contact homology VIII

Series
Geometry Topology Working Seminar
Time
Friday, April 5, 2013 - 11:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
In this series of talks I will begin by discussing the idea of studying smooth manifolds and their submanifolds using the symplectic (and contact) geometry of their cotangent bundles. I will then discuss Legendrian contact homology, a powerful invariant of Legendrian submanifolds of contact manifolds. After discussing the theory of contact homology, examples and useful computational techniques, I will combine this with the conormal discussion to define Knot Contact Homology and discuss its many wonders properties and conjectures concerning its connection to other invariants of knots in S^3.

On Adam Jakubowski's approach to proving asymptotic results for regularly varying sequences

Series
Stochastics Seminar
Time
Thursday, April 4, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thomas Mikosch – University of Copenhagen
In recent work, an idea of Adam Jakubowski was used to prove infinite stable limit theory and precise large deviation results for sums of strictly stationary regularly varying sequences. The idea of Jakubowski consists of approximating tail probabilities of distributions for such sums with increasing index by the corresponding quantities for sums with fixed index. This idea can also be made to work for Laplace functionals of point processes, the distribution function of maxima and the characteristic functions of partial sums of stationary sequences. In each of these situations, extremal dependence manifests in the appearance of suitable cluster indices (extremal index for maxima, cluster index for sums,...). The proposed method can be easily understood and has the potential to function as heuristics for proving limit results for weakly dependent heavy-tailed sequences.

Quasirandom Hypergraphs

Series
Graph Theory Seminar
Time
Thursday, April 4, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dhruv Mubayi – University of Illinois at Chicago
Since the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs over 20 years ago, there has been a lot of effort by many researchers to extend the theory to hypergraphs. I will present some of this history, and then describe our recent results that provide such a generalization and unify much of the previous work. One key new aspect in the theory is a systematic study of hypergraph eigenvalues first introduced by Friedman and Wigderson. This is joint work with John Lenz.

CANCELLED: Minimal Energy and Maximal Polarization

Series
School of Mathematics Colloquium
Time
Thursday, April 4, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ed Saff – Vanderbilt University
While this could be a lecture about our US Congress, it instead deals with problems that are asymptotically related to best-packing and best-covering. In particular, we discuss how to efficiently generate N points on a d-dimensional manifold that have the desirable qualities of well-separation and optimal order covering radius, while asymptotically having a prescribed distribution. Even for certain small numbers of points like N=5, optimal arrangements with regard to energy and polarization can be a challenging problem.

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